OFFSET

1,2

COMMENTS

For general Modd n (not to be confused with mod n) see a comment on A203571. The present sequence gives the residues Modd 15 of the positive odd numbers relatively prime to 15 (the positive odd numbers from all reduced residue classes mod 15), shown in A007775. The underlying periodic sequence with period length 30 is [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,0,14,13,12,11,10,9,8,7,6,5,4,3,2,1], called, with offset 0, P_15 or Modd15.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..8192

Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,1,-1,1).

FORMULA

a(n) = A007775(n) (Modd 15) := Modd15(A007775(n)), n>=1, with the periodic sequence Modd15 (period length 30) given in the comment section.

O.g.f: x*(1+x^7+7*x*(1+x^5)+11*x^2*(1+x^3)+13*x^3*(1+x))/(1-x^8) = x*(1+x)*(1+6*x+5*x^2+8*x^3+5*x^4+6*x^5+x^6)/(1-x^8).

a(n) = -k^2 + 7k + 1 where k = (n-1) mod 8. - David A. Corneth, Aug 13 2017

EXAMPLE

Residues Modd 15 of the positive odd numbers relatively prime to 15:

A007775: 1, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, ...

Modd 15: 1, 7, 11, 13, 13, 11, 7, 1, 1, 7, 11, 13, 13, 11, ...

MATHEMATICA

PadRight[{}, 100, {1, 7, 11, 13, 13, 11, 7, 1}] (* Harvey P. Dale, Sep 30 2015 *)

PROG

(PARI) a(n)=[1, 7, 11, 13, 13, 11, 7, 1][n%8+1] \\ Charles R Greathouse IV, Jul 17 2016

(Scheme) (define (A206546 n) (list-ref '(1 7 11 13 13 11 7 1) (modulo (- n 1) 8))) ;; Antti Karttunen, Aug 10 2017

CROSSREFS

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Feb 10 2012

STATUS

approved